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Books - Science - Mathematics - Mathematical Analysis - For the Aspiring Analyst |
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Elementary Classical Analysis by Jerrold E. Marsden, Michael J. Hoffman Average Customer Review: Hardcover (15 March, 1993) list price: $108.95 -- our price: $108.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (9)
Don't see why its used in so many classrooms
Not So Hot.
An excellent introduction to Real Analysis "We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs." Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable. A side note: Though Marsden and Hoffman do make light of Cantor's quaint, 19th century definition of a set in their intro to set theory, they ultimately do so only to motivate the exposition of a formal, axiomatic view. ... Read more Isbn: 0716721058 |
$108.95 |
Elementary Real and Complex Analysis (Dover Books on Mathematics) by Georgi E. Shilov, Richard A. Silverman Average Customer Review: Paperback (01 February, 1996) list price: $19.95 -- our price: $13.57 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (6)
Getting started in math analysis
Possibly too simple However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin.
A wonderful text -- Highly recommended! As far as the actual material presented, Dr. Shilov starts off with funtions of one real variable, then rather quickly generalizes to complex variables and N dimensional functions, so you'll quickly see metric theory and some topology.He does keep in mind this is intended for undergrads and first year grads though. Oh, another nice feature is the price!I'd recommend this book to any math enthusiast as a reference, or to someone going through an early analysis course. ... Read more Isbn: 0486689220 |
$13.57 |
Mathematical Analysis (2nd Edition) by Tom M. Apostol Average Customer Review: Paperback (01 January, 1974) list price: $119.40 -- our price: $119.40 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (15)
One of the best I own...
The Cat's Meow
A cut above the rest... One drawback to the text is a too abstract approach to the Implict and Inverse Function Theorems. I found these to be the most challenging in the text, and I was forced to return to my copy of Stewart's Calculus text to re-acquiant myself with each concept. Also, at times Apostol falls into the pattern of Definition, Theorem, Definition, Theorem,..., but this seems to be only in the cases when ample preparation is needed to provide noteworthy examples; eg. Lebesgue integration. So, in spite of the cost, I highly recommend this text for the study of real analysis (even for self study), although at [this price] there are bound to be others that have a higher value to cost ratio. Having completed the text (almost), I feel prepared to begin a more abstract study of analysis. ... Read more Isbn: 0201002884 |
$119.40 |
Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by WalterRudin Average Customer Review: Hardcover (01 January, 1976) list price: $138.13 -- our price: $138.13 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (73)
An excellent textbook
A masterpiece
Great analysis... Isbn: 007054235X |
$138.13 |
Topology (2nd Edition) by James Munkres Average Customer Review: Hardcover (28 December, 1999) list price: $106.67 -- our price: $106.67 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (24)
The best rigorous introduction to general topology!
great!
Excellent Topology Book Later at graduate school, Munkres was also used in a topology class at the beginning graduate level.Highlights were taken from the first section (point set topology), and a large focus of the class was on the algebraic topology in the second section of the book.Sometimes I had difficulty following exactly what the professor was doing at the blackboard, but I could always understand what was going on when I consulted Munkres. I would stress that this is only to be used as an introduction to algebraic topology, as there is nearly no development of homology groups and other algebraic concepts.However, it gives a very good presentation for the fundamental group.As a whole it would be a very good addition to your mathematical library. ... Read more Isbn: 0131816292 |
$106.67 |
The Way of Analysis (Jones and Bartlett Books in Mathematics) by Robert S. Strichartz Average Customer Review: Paperback (01 June, 2000) list price: $86.95 -- our price: $86.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (16)
Lots of description... a bit too much
Very lucid and ideal material for learning real analysis
The best to understand and do Analysis Isbn: 0763714976 |
$86.95 |
Undergraduate Analysis (Undergraduate Texts in Mathematics) by Serge Lang Average Customer Review: Hardcover (May, 2005) list price: $69.95 -- our price: $59.48 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
Just like every other Lang text
Solid, complete reference to basic analysis topics
okay Isbn: 0387948414 |
$59.48 |
Principles of Real Analysis by Charalambos D. Aliprantis, Owen Burkinshaw Average Customer Review: Hardcover (15 September, 1998) list price: $98.95 -- our price: $98.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (3)
Excellent Coverage plus a wealth of problems
Very Mediocre Contents, Terrible Aesthetics
One of the best Isbn: 0120502577 |
$98.95 |
Real Analysis (3rd Edition) by Halsey Royden Average Customer Review: Hardcover (02 February, 1988) list price: $114.67 -- our price: $114.67 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (17)
Standard Analysis Text; Necessary, but not Sufficient!
this book is just plain good.
Not bad for self-study, excellent for reference Isbn: 0024041513 |
$114.67 |
Real and Complex Analysis (Higher Mathematics Series) by WalterRudin Average Customer Review: Hardcover (01 May, 1986) list price: $140.94 -- our price: $140.94 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (16)
A start in math. The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory. I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know. What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting. Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well. After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!" Review by Palle Jorgensen, September 2004.
Welcome to the self-service analysis center! Also, Rudin does not discuss some of the more advanced or interdisciplinary topics such as distribution theory (Sobolev spaces, weak derivatives, etc.) or applications of measure theory to the probability theory, both explored in the book by Folland. Last but not least, it's worth noting that contrary to the common practice, Folland includes many end-of-chapter notes where he outlines some important historical aspects of the development of the topics, and also gives a few references for further study. For example, in the notes section at the end of the chapter on Lebesgue integration, he mentions --and briefly outlines-- the basics of the theory of "gauge integration" (also called Henstock-Kurzweil theory) which serves to construct a more powerful integral than that of the Lebesgue's. As another instance, having already defined and used "nets" within the chapter on topology, in the end-notes Folland also introduces "filters" and "ultrafilters". These are all machineries which have been developed to play the role of the metric space sequences in general (locally Hausdorff) topological spaces, but for some historical reasons, ultrafilters have nowadays taken a backseat to the nets (the older general topology books usually prove the Tychonoff theorem using ultrafilters). All said, I can recommend taking up Royden as your very first approach to measure theory, then based on how well you think you have learned the first course, move on to either Rudin or Folland for a more advanced treatment. Please note that the other books I have mentioned above do not discuss complex analysis, a subject which is also masterfully presented in Rudin. There are however a few other equally well-written complex analysis books to pick from, for example John B. Conway's classic from the Springer-Verlag graduate series, or L.V. Ahlfors' masterpiece, to name just a couple.
A Comprehensive Guide to Analysis For example, the construction of Lebesgue measure is considered one of the most important topics in graduate analysis courses.After this construction, more abstract measures are developed, and then one proves the Riesz Representation Theorem for positive functionals later. Conversely, Rudin develops a few basic topological tools, such as Urysohn's Theorem and a finite partition of unity, to construct the Radon measure needed in a sweeping proof of Riesz's Theorem.From this, results about regularity follow clearly, and the construction of Lebesgue measure involves little more than a routine check of its invariance properties. Another example of where Rudin takes a more theoretical approach to provide a more elegant, yet less intuitive proof, is the Lebesgue-Radon-Nikodym theorem.Other books generally introduce signed measures with several examples, and use this result, along with properties of measures to derive the proof.On the other hand, since the first half of the book contains an intermission on Hilbert Space, Rudin uses the completeless of L^2 and the Riesz Representation Theorem for a more sweeping proof. In the real analysis section, Rudin covers advanced topics generally not covered in a first course on measure theory.The chapters on differentiation and Fourier analysis are key examples of this.Rudin uses maximal functions to develop the Lebesgue Point theorem and results from complex analysis, and provides an incredibly thorough proof of the change-of-variables theorem.The ninth chapter, on Fourier transforms, relies heavily on convolutions, which are developed as a product of Fubini's theorem.This, in turn, is used to prove Plancherel's theorem and the uniqueness of Fourier transforms as a character homomorphism. The tenth chapter, on basic complex analysis, essentially covers an entire undergraduate course on the subject, with added results based on a solid knowledge of topology on the plane.Once a solid foundation on the topic is laid, Rudin can develop more advanced topics from Harmonic analysis using general results from real analysis like the Hahn-Banach theorem and the Lebesgue Point theorem (for Poisson integrals). Most of the basic results from the power series perspective are covered in the text, but while the geometric view is examined, it is still done in a very analytic, formula-based way that does not allow the reader to gain too much intuition.Nonetheless, all the basic results are covered, and Rudin uses these to develop the main theorems, such as the Mittag-Leffler and Weierstrass theorems on meromorphic functions, and the Monodromy Theorem and a modular function used to prove Picard's Little Theorem. As an introductory text, even for advanced students, Rudin should probably be accompanied by more descriptive texts to develop better intuition.In fact, I would recommend Folland's Real Analysis and Ahlfors' Complex Analysis for self-study, because the problems are easier and one can learn better through those.With a good instructor, though, Rudin's text is concise and elegant enough to be both useful and enjoyable.It is also a good test to see how well one REALLY knows the subject. ... Read more Isbn: 0070542341 |
$140.94 |
Basic Complex Analysis by Jerrold E. Marsden, Michael J. Hoffman Average Customer Review: Hardcover (15 December, 1998) list price: $108.95 -- our price: $119.49 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (12)
Quite Dry The examples of the book are quite simple, compare to some end of section problems. Overall this book has no surprises as it is quite dry, got bored from reading it.If it was not a required text book for a 3rd year complex analysis course, i wouldn't recommend it to anyone.There are many other books out there that are better written.
A versatile introduction to the subject. The book is clearly written and well-organized, with plenty of examples and exercises.My only significant criticism of the first edition was the author's tendency to label many examples of contour integration as theorems.Technically, there is nothing wrong this, but I found that some of my students tended to memorize the statements of these "theorems" rather than focus on the methods of integration discussed (for example, "Pac-Man" integrals with branch cuts along rays other than the positive real axis).Nonetheless, this is a fine text that has--not surprisingly--continued to be widely used for over two decades.
Mediocre Textbook! Isbn: 071672877X |
$119.49 |
Complex Analysis (Graduate Texts in Mathematics) by Serge Lang Average Customer Review: Hardcover (15 January, 1999) list price: $69.95 -- our price: $59.83 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
sweet dude
A good book, but not for beginners.
Not TOO complex A brief discriptionof the chapters (some of them at least): Chp 1:basic definitions &operations, polar form, functions, limits, compact sets, differentiation,Cauchy-Riemann eqs, angles under holomorphic ("differentiable")maps. Chp 2:formal & convergent power series, analytic functions,inverse & open mapping thms., local maximum modulus principle Chp 3: connected sets, integrals over paths, primitives("antiderivatives"), local Cauchy thm, etc Chp 4:windingnumbers, global Cauchy Thm, Artin's proof Chp 5:Applications ofCauchy's integral formula, Laurent series Chp 6:Calculus of residues,evaluation of complex definate integrals, Fourier transforms, etc(funstuff) Chp 7: Comformal mapping, Schwarz lemma, analytic automorphisms ofthe Disc Chp 8:Harmonic functions; Chp 9: Schwarz reflection; Chp 10: Riemann mapping theorem; (11):Analytic continuation along curves; (12)applications of Maximum Modulus Principle an Jensen's Formula; (13)Entire& Meromorphic functions; (14) elliptic functions; (15) Gamma & Zetafunctions; (16) The Prime Number Theorem; and a handy appendix. ... Read more Isbn: 0387985921 |
$59.83 |
Beginning Functional Analysis by Karen Saxe Average Customer Review: Hardcover (07 December, 2001) list price: $44.95 -- our price: $44.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
I'm Sorry
Quite a bad book.
Lucid One thing I especially enjoyed about this book is that most of the proofs are done only for special cases of theorems, without loss of generality. For example, the Arzela-Ascoli theorem is proved for the function space C([a,b],R) (R = real numbers), but then Saxe points out what makes the proof 'tick' so that the reader may easily modify it to a more general setting (she always states the more precise versions of such theorems as well). This is great because it helps one's intuition without getting short-changed. Finally, the book has a great wealth of historical notes and biographies which are rich in mathematical content (e.g., Saxe explains that Frechet was the first person to define a metric space even though he called it 'une class E'; Hausdorff gave it its modern name in 1914). The reader can in this way appreciate how the subject slowly developed into its present form. This book is a jewel! I myself am not the biggest fan of functional analysis, but this book made me really appreciate the subject. ... Read more Isbn: 0387952241 |
$44.95 |
Introductory Functional Analysis with Applications by ErwinKreyszig Average Customer Review: Paperback (23 February, 1989) list price: $71.95 -- our price: $71.95 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (7)
The best undergraduate introduction to the subject
The definition of classic
Possibly the BEST math book that I have ever read Isbn: 0471504599 |
$71.95 |
Functional Analysis by WalterRudin Average Customer Review: Hardcover (01 January, 1991) list price: $131.56 -- our price: $131.56 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (4)
Decent book, if you can get it cheap With that said, I don't like this book as much.Perhaps because the problems don't provide great movitation for the theorems- in any event, I would recommend using at least two books to understand functional analysis.One that emphasizes a rigorous approach to the theory involved, and another more applied book that allows you to play with the new tools to solve the problems functional analysis was invented to solve; quantum mechanics, for example. Reed and Simon is a good book, although I'm sure physicists or physics students would probably complain about it for the same reason I like it- its very mathematically rigorous and has a ton of problems- 30 to 60 on average at the end of each chapter, with only a few digressions into applications into quantum physics or elementary QFT.Get this with some Springer text, like Elements of Functional Analysis. One more note- Rudin's book is broken up into three parts- one on TVS (Topological vector spaces) that combines topological properties of a space (for example, local convexity or local compactness) with the usual vector-space operations to set the spaces where operators act. The second section deals with distributions- I regret that one failure of "Adult Rudin" was to emphasize the abstract integral as a linear functional, because this would have helped to make the concept of a distribution more clear. While the introduction to distributions and their connections to Fourier analysis and differential equations is nice, the text gets bogged down with proofs about convolutions that are highly technical (and make either good practice or a good time for Rudin to actually use, for once, "The details are left to the reader..."). Finally, Rudin introduces operator theory, although it could go much more smoothly- the proofs come off as way too technical, a far cry from the "slickness" his proofs are often accused of being in the graduate analysis text. All in all, there's some interesting problems to do, but you're not going to understand the applications of Functional Analysis to quantum mechanics or PDE (other than distributions a little), where other, more applied (read: easier) books may give nice problems about applications of Hilbert space methods, such as variational techniques or Fredholm theory.
Modern topics in math.
The Bible on Distributions Isbn: 0070542368 |
$131.56 |
Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) by Peter D.Lax Average Customer Review: Hardcover (22 March, 2002) list price: $105.00 -- our price: $91.71 (price subject to change: see help) US | Canada | United Kingdom | Germany | France Reviews (2)
Excellent
Brings the subject to life! quantum theory, for dynamical systems, and for partial differential equations. The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor Isbn: 0471556041 |
$91.71 |
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